{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Probabilistic PCA\n",
    "\n",
    "Probabilistic principal components analysis (PCA) is a\n",
    "dimensionality reduction technique that\n",
    "analyzes data via a lower dimensional latent space\n",
    "(Tipping & Bishop, 1999). It is often\n",
    "used when there are missing values in the data or for multidimensional\n",
    "scaling.\n",
    "\n",
    "We demonstrate with an example in Edward. A webpage version is available at\n",
    "http://edwardlib.org/tutorials/probabilistic-pca."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from __future__ import absolute_import\n",
    "from __future__ import division\n",
    "from __future__ import print_function\n",
    "\n",
    "import edward as ed\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import tensorflow as tf\n",
    "\n",
    "from edward.models import Normal\n",
    "\n",
    "plt.style.use('ggplot')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data\n",
    "\n",
    "We use simulated data. We'll talk about the individual variables and\n",
    "what they stand for in the next section. For this example, each data\n",
    "point is 2-dimensional, $\\mathbf{x}_n\\in\\mathbb{R}^2$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True principal axes:\n",
      "[[ 0.25947927]\n",
      " [ 1.80472372]]\n"
     ]
    }
   ],
   "source": [
    "def build_toy_dataset(N, D, K, sigma=1):\n",
    "  x_train = np.zeros((D, N))\n",
    "  w = np.random.normal(0.0, 2.0, size=(D, K))\n",
    "  z = np.random.normal(0.0, 1.0, size=(K, N))\n",
    "  mean = np.dot(w, z)\n",
    "  for d in range(D):\n",
    "    for n in range(N):\n",
    "      x_train[d, n] = np.random.normal(mean[d, n], sigma)\n",
    "\n",
    "  print(\"True principal axes:\")\n",
    "  print(w)\n",
    "  return x_train\n",
    "\n",
    "ed.set_seed(142)\n",
    "\n",
    "N = 5000  # number of data points\n",
    "D = 2  # data dimensionality\n",
    "K = 1  # latent dimensionality\n",
    "\n",
    "x_train = build_toy_dataset(N, D, K)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We visualize the data set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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9aGtrw9DQ0JzPP/LII3j00UenPdbS0oKrrroK4XAYS5yAYRYRl8uFeDy+1MtY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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11640b410>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x_train[0, :], x_train[1, :], color='blue', alpha=0.1)\n",
    "plt.axis([-10, 10, -10, 10])\n",
    "plt.title(\"Simulated data set\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Model\n",
    "\n",
    "Consider a data set $\\mathbf{X} = \\{\\mathbf{x}_n\\}$ of $N$ data\n",
    "points, where each data point is $D$-dimensional, $\\mathbf{x}_n \\in\n",
    "\\mathbb{R}^D$. We aim to represent each $\\mathbf{x}_n$ under a latent\n",
    "variable $\\mathbf{z}_n \\in \\mathbb{R}^K$ with lower dimension, $K <\n",
    "D$. The set of principal axes $\\mathbf{W}$ relates the latent variables to\n",
    "the data.\n",
    "\n",
    "Specifically, we assume that each latent variable is normally distributed,\n",
    "\n",
    "\\begin{equation*}\n",
    "\\mathbf{z}_n \\sim N(\\mathbf{0}, \\mathbf{I}).\n",
    "\\end{equation*}\n",
    "\n",
    "The corresponding data point is generated via a projection,\n",
    "\n",
    "\\begin{equation*}\n",
    "\\mathbf{x}_n \\mid \\mathbf{z}_n\n",
    "\\sim N(\\mathbf{W}\\mathbf{z}_n, \\sigma^2\\mathbf{I}),\n",
    "\\end{equation*}\n",
    "\n",
    "where the matrix $\\mathbf{W}\\in\\mathbb{R}^{D\\times K}$ are known as\n",
    "the principal axes. In probabilistic PCA, we are typically interested in\n",
    "estimating the principal axes $\\mathbf{W}$ and the noise term\n",
    "$\\sigma^2$.\n",
    "\n",
    "Probabilistic PCA generalizes classical PCA. Marginalizing out the the\n",
    "latent variable, the distribution of each data point is\n",
    "\n",
    "\\begin{equation*}\n",
    "\\mathbf{x}_n \\sim N(\\mathbf{0}, \\mathbf{W}\\mathbf{W}^T + \\sigma^2\\mathbf{I}).\n",
    "\\end{equation*}\n",
    "\n",
    "Classical PCA is the specific case of probabilistic PCA when the\n",
    "covariance of the noise becomes infinitesimally small, $\\sigma^2 \\to 0$.\n",
    "\n",
    "We set up our model below. In our analysis, we fix $\\sigma=2.0$, and\n",
    "instead of point estimating $\\mathbf{W}$ as a model parameter, we\n",
    "place a prior over it in order to infer a distribution over principal\n",
    "axes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "w = Normal(loc=tf.zeros([D, K]), scale=2.0 * tf.ones([D, K]))\n",
    "z = Normal(loc=tf.zeros([N, K]), scale=tf.ones([N, K]))\n",
    "x = Normal(loc=tf.matmul(w, z, transpose_b=True), scale=tf.ones([D, N]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Inference\n",
    "\n",
    "The posterior distribution over the principal axes $\\mathbf{W}$ cannot\n",
    "be analytically determined. Below, we set up our inference variables\n",
    "and then run a chosen algorithm to infer $\\mathbf{W}$. Below we use\n",
    "variational inference to minimize the $\\text{KL}(q\\|p)$ divergence\n",
    "measure."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "500/500 [100%] ██████████████████████████████ Elapsed: 7s | Loss: 17802.207\n"
     ]
    }
   ],
   "source": [
    "qw = Normal(loc=tf.get_variable(\"qw/loc\", [D, K]),\n",
    "            scale=tf.nn.softplus(tf.get_variable(\"qw/scale\", [D, K])))\n",
    "qz = Normal(loc=tf.get_variable(\"qz/loc\", [N, K]),\n",
    "            scale=tf.nn.softplus(tf.get_variable(\"qz/scale\", [N, K])))\n",
    "\n",
    "inference = ed.KLqp({w: qw, z: qz}, data={x: x_train})\n",
    "inference.run(n_iter=500, n_print=100, n_samples=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Criticism\n",
    "\n",
    "To check our inferences, we first inspect the model's learned\n",
    "principal axes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Inferred principal axes:\n",
      "[[-0.24093632]\n",
      " [-1.76468039]]\n"
     ]
    }
   ],
   "source": [
    "sess = ed.get_session()\n",
    "print(\"Inferred principal axes:\")\n",
    "print(sess.run(qw.mean()))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The model has recovered the true principal axes up to finite data and\n",
    "also up to identifiability (there's a symmetry in the\n",
    "parameterization).\n",
    "\n",
    "Another way to criticize the model is to visualize the observed data\n",
    "against data generated from our fitted model. The blue dots represent\n",
    "the original data, while the red is the inferred."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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plW7098OOxWBkMtA+H4kCv58qNaqjBJOJBHeCrZ5ohQCyWUjH3nsmEQ/3LV5q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UJbKkHYVFFdLkMGAWPJq1WYXo+GYEEAE8fQu7sIPv+8kLKiVoMejciPGI+R/fZvA6enbDbKZZT+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\n5E2iZreO53GsaNw6E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      "text/plain": [
       "<matplotlib.figure.Figure at 0x11650bf50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Build and then generate data from the posterior predictive distribution.\n",
    "x_post = ed.copy(x, {w: qw, z: qz})\n",
    "x_gen = sess.run(x_post)\n",
    "\n",
    "plt.scatter(x_gen[0, :], x_gen[1, :], color='red', alpha=0.1)\n",
    "plt.axis([-10, 10, -10, 10])\n",
    "plt.title(\"Data generated from model\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The generated data looks close to the true data.\n",
    "\n",
    "## Acknowledgements\n",
    "\n",
    "We thank Mayank Agrawal for writing the initial version of this\n",
    "tutorial."
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
